An AWG multiplexer should normally be stabilized/temperature controlled with a heater or a Peltier cooler to stabilize the channel wavelengths. This requires a constant electric power consumption of several watts and other equipment for temperature control. With reference to FIG. 1, a typical AWG 10 is shown having similarly-formed input 12 and output 14 slab waveguide regions. FIG. 1 also shows a technique for thermal stabilization involving a mechanical compensation approach. In this approach, the input waveguide is cut off at the interface between input node and the slab region 12. The separated input chip is attached to a metal rod 20, which is fixed to a stable post. The metal rod changes length with ambient temperature and shifts the input waveguide along the interface of the slab waveguide 12 to compensate for the thermal drift of the pass wavelength in AWG.
The present invention addresses the problem of tight alignment tolerances when the movable chip to which the metal rod is fixed is attached to the slab region of an AWG.
An effective wavelength in the array waveguide at T is given by λ0/nc(T), where nc=βc/k (βc: propagation constant of the waveguide). When temperature is changed from T to T+ΔT, the effective index nc becomes nc(T+ΔT)=nc(T)+ΔT·dnc/dT. Temperature dependence of nc in silica glass is dnc/dT=1.1×10−5 (1/deg). The effective wavelength in the waveguide at T+ΔT is expressed by:
                                          λ            0                                              n              c                        ⁡                          (                              T                +                                  Δ                  ⁢                                                                          ⁢                  T                                            )                                      =                                            λ              0                                                                        n                  c                                ⁡                                  (                  T                  )                                            +                                                                                          ⅆ                                              n                                                  c                          ⁢                                                                                                                                                                                            ⅆ                      T                                                        ·                  Δ                                ⁢                                                                  ⁢                T                                              ≅                                                                      λ                  0                                -                                                                            λ                      0                                                              n                      c                                                        ⁢                                                                                    ⅆ                                                  n                          c                                                                                            ⅆ                        T                                                              ·                    Δ                                    ⁢                                                                          ⁢                  T                                                                              n                  c                                ⁡                                  (                  T                  )                                                      .                                              (        1        )            
It is known from Eq. (1) that the effective-index variation by the temperature change ΔT is equivalent to the wavelength change Δλ in an amount of:
                              Δ          ⁢                                          ⁢          λ                =                              -                                          λ                0                                            n                c                                              ⁢                                                    ⅆ                                  n                  c                                                            ⅆ                T                                      ·            Δ                    ⁢                                          ⁢                      T            .                                              (        2        )            
Since the dispersion of the focal position x with respect to the wavelength change is given by K. Okamoto, Fundamentals of Optical Waveguides, 2nd Edition (Elsevier, N.Y., 2006) chapter 9, as:
                                                        Δ              ⁢                                                          ⁢              x                                      Δ              ⁢                                                          ⁢              λ                                =                      -                                                            N                  c                                ⁢                f                ⁢                                                                  ⁢                Δ                ⁢                                                                  ⁢                L                                                              n                  s                                ⁢                                  d                                      λ                    0                                                                                      ,                            (        3        )            a shift of the focal position x with respect to the temperature variation is obtained by:
                              Δ          ⁢                                          ⁢          x                =                                                            N                c                            ⁢              f              ⁢                                                          ⁢              Δ              ⁢                                                          ⁢              L                                                      n                s                            ⁢              d                                ·                                    ⅆ                              n                c                                                    ⅆ              T                                ·                                                    Δ                ⁢                                                                  ⁢                T                                            n                c                                      .                                              (        4        )            
On the other hand the thermal expansion of the compensating rod shifts the input waveguide by:Δx1=−(αrod−αchip)LΔT,  (5)where L is the length of the compensating rod, and αrod and αchip are thermal expansion coefficients of the metal rod and AWG chip (αrod>αchip), respectively. When the input waveguide is shifted by Δx1, the focal position at the output side moves by Δx*=Δx1. When Δx*=−Δx holds, shift of the focal position due to temperature change is canceled out. The athermal condition for the length of the metal rod L is obtained by using Eqs. (4) and (5) by:
                                          (                                          α                rod                            -                              α                chip                                      )                    ⁢          L                =                                                                              N                  c                                ⁢                f                ⁢                                                                  ⁢                Δ                ⁢                                                                  ⁢                L                                                              n                  s                                ⁢                d                                      ·                          1                              n                c                                              ⁢                                                    ⅆ                                  n                  c                                                            ⅆ                T                                      .                                              (        6        )            
The shift of the focal position is about Δx=±19.4 μm for the temperature variation of ΔT=±50° C. centered at 20° C. for a typical AWG with input/output waveguide spacing at the slab interface D=27 μm, array waveguide spacing at the slab-array interface d=15 μm, focal length of first and second slab f=19.854 mm, path length difference ΔL=31.0 μm, channel spacing Δλ=0.8 nm (100 GHz), number of channels N=64, and operating wavelength λ0=1.55 μm.
When attaching the movable chip to the original AWG chip, the alignment of the input waveguide to the proper position of the first slab region requires fine accuracy. Typical center wavelength accuracy for a 100-GHz AWG is ±0.032 nm (±5 GHz). This corresponds to a positional accuracy of ±1 μm since input/output waveguide spacing D=20 μm corresponds to the channel spacing of 0.8 nm (100 GHz). Because alignment accuracy of ±1 μm is very tight, any failure of the initial alignment and glue process easily leads to out-of-specification center wavelength (frequency). This is the major reason for lower yields and higher costs of mechanically athermalized AWGs.
The present invention achieves larger alignment tolerances, to thereby achieve higher yields and lower costs for athermal AWGs.